We construct exceptional collections of maximal length on four families of surfaces of general type with pg = q = 0 which are isogenous to a product of curves. From these constructions we obtain new examples of quasiphantom categories as their orthogonal complements.Question. Let S be a smooth projective surface of general type with p g = q = 0. Is there an exceptional sequence whose length is equal to the rank of Grothendieck Key words and phrases. Derived category, exceptional sequence, quasiphantom category, surfaces of general type, surfaces isogenous to a higher product.
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